Summary of this paper

• US Minnesota Twin Study Sample
• Build a genetic model of human capital investments with genotype transmission (with better genetics foundation than ad hoc standard econ models)
• Intergenerational elaciticity of income is predicted to be larger in genetic models
• Empirical pathway: Through parental education and incomes, parental PGS has no direct effect on child human capital
• Child PGS is relevant
• Genetic nurture (introverted genotype produces an environment to grow introverted child, independently of income and education) is not found

SNP, polygenic score

.
└── Chromosome
    └── DNA
        └── Gene
            └── Genome

• Base pairs differ between people in less than 1% (15 million) locations
  
• Single-nucleotide polymorphism (SNP) = such location
  • 2 chromosomes per person → AT-AT, GC-GC, AT-GC or 0, 2, 1 (reference = GC)

Twin studies

• Estimate how much genetic factors collectively matter for explaining variations of a trait
  • Collectively: Unit = group level aggregation
  • Explaining variations: Variance decomposition
• Do not reveal which SNP is correlated

Genome wide association studies (GWASs)

• Collect \(M\) observable (?) SNPs of (family \(i\)) individual \(j\).

Polygenic score = Predicted outcomes based on all relevant SNPs

\[ PGS^{i}_{j}=\sum_{m=1}^{M}\tilde{\beta}_{m} SNP^{i}_{jm} \]

• Use Bayesian LDpred procedure to correct for correlations in \(\tilde{\beta}_{m}\)
  • Barth, Papageorge, and Thom (2020) follow the convention and use all SNPs: Better out-of-sample results than using only SNPs with genome-wide significance \(p\) value \(< 5*10^{-8} =\) .0000005%
• PGS is considered to be a predictor of individual fixed effects
  • Edu attainment SNPs \(\SIM\) biological process of brain development, cognition (Okbay et al. 2016; Lee et al. 2018)
  • Edu attainment SNPs \(\SIM\) cognition SNPs (Okbay et al. 2016)
  • HRS sample: cov[EA score, schooling years] / variance[schooling years] = 10.6%

Intergenerational skill formation

• Becker and Tomes (1979): AR(1)
• Goldberger (1989): Weighted average of all ancestors
• Both are incorrect, this paper shows there exists an invariant (stable) mapping father genotype distribution × mother genotype distribution \(\to\) child genotype distribution, so skill formation depends on parental genotype distributions

Matching of parents

• Assume independence of genotype conditional on observable characteristics [incomes, skills \(w(g)\)]
  • Matches are made on observables, not on genotype
  • Matches are random within obserbable strata “worth” classes=\(w_{\mathrm{y}}y+w(g)\)]
    • Genotype matching is random within a stratum
  • Matches are nonrandom at the population due to population stratification based on observables

Skills production function (genotype enters here, hence the parental genotypes) \[ \theta^{i}_{j}=w\left(g^{i}_{j}\right)+\pi y^{i}+\bfPi\bfx^{i}_{j}+F^{i}+\epsilon^{\theta i}_{j} \tag{4}\label{eq4} \] Estimating equations: Substitute [4] into [12] gives child income decomposition, and [11] into [8] gives human capital decomposition \[ \begin{align} y^{i}_{j} &= \alpha_{\theta}\alpha_{\mathrm{h}}w\left(g^{i}_{j}\right) +\left(\alpha_{\mathrm{I}}\alpha_{\mathrm{h}}+\alpha_{\theta}\alpha_{\mathrm{h}}\pi\right)y^{i} +\alpha_{\theta}\alpha_{\mathrm{h}}F^{i}\\ &\hspace{1em} +\alpha_{\theta}\alpha_{\mathrm{h}}\bfPi\bfx^{i}_{j} +\alpha_{\theta}\alpha_{\mathrm{h}}\epsilon^{\theta i}_{j} +\alpha_{\mathrm{h}}\epsilon^{\mathrm{h} i}_{j} +\epsilon^{\mathrm{y}i}_{j}\tag{21}\label{eq21}\\ h^{i}_{j} &= \alpha_{\theta}w\left(g^{i}_{j}\right) +\left(\alpha_{\mathrm{I}}+\alpha_{\theta}\pi\right)y^{i} +\alpha_{\theta}F^{i}\\ &\hspace{1em} +\alpha_{\theta}\bfPi\bfx^{i}_{j} +\alpha_{\theta}\epsilon^{\theta i}_{j} +\epsilon^{\mathrm{y}i}_{j}\tag{23}\label{eq23} \end{align} \]

Can show IGE is smaller in “standard model” than genetic model

Structural equation model (SEM)

• Structural equations
• Measurement (error) equations

Identification ideas

1. Dizygotic twins [Table 1, 2]
   • Share birth days, environment
   • Differ in genotypes
   • Ideal to see impacts of genotypes on outcomes

Identification ideas

2. SEM
   • Recursive system (37)-(42) are identified as usual [Table 2]
   • Structural parameters of endogenous variables are recovered from [eq43]-[eq45] (how?) [Table 3]
     • Given PGS of child, PGS of parents should be redundant, so long as they do not affect environment (gene-environment correlation, or “passive rGE”)

感想

• 咀嚼できていません
• 人的資本投資を内生化したsteady state genetic transmission mappingの存在を証明
• それと実証部分の結びつきが弱い(理解できていない)
• 親の教育と所得を考慮すると、遺伝情報は子の教育に影響しないことを実証的に示したのは斬新
• SEMはidentification assumptionが不明(recursiveモデル以外)、IVを使っていない?
• Multiple testing気にせず